@article{SM_2021_212_9_a1,
author = {Ya. M. Dymarskii and A. A. Bondar'},
title = {An eigenfunction manifold generated by a~family of periodic boundary value problems},
journal = {Sbornik. Mathematics},
pages = {1208--1227},
year = {2021},
volume = {212},
number = {9},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2021_212_9_a1/}
}
TY - JOUR AU - Ya. M. Dymarskii AU - A. A. Bondar' TI - An eigenfunction manifold generated by a family of periodic boundary value problems JO - Sbornik. Mathematics PY - 2021 SP - 1208 EP - 1227 VL - 212 IS - 9 UR - http://geodesic.mathdoc.fr/item/SM_2021_212_9_a1/ LA - en ID - SM_2021_212_9_a1 ER -
Ya. M. Dymarskii; A. A. Bondar'. An eigenfunction manifold generated by a family of periodic boundary value problems. Sbornik. Mathematics, Tome 212 (2021) no. 9, pp. 1208-1227. http://geodesic.mathdoc.fr/item/SM_2021_212_9_a1/
[1] Ya. M. Dymarskii, Yu. A. Evtushenko, “Foliation of the space of periodic boundary-value problems by hypersurfaces corresponding to fixed lengths of the $n$th spectral lacuna”, Sb. Math., 207:5 (2016), 678–701 | DOI | DOI | MR | Zbl
[2] F. Neuman, “Linear differential equations of the second order and their applications”, Rend. Mat. (6), 4 (1971), 559–617 | MR | Zbl
[3] E. L. Ince, “Periodic solutions of a linear differential equation of the second order with periodic coefficients”, Proc. Cambridge Philos. Soc., 23:1 (1927), 44–46 | DOI | Zbl
[4] K. Uhlenbeck, “Generic properties of eigenfunctions”, Amer. J. Math., 98:4 (1976), 1059–1078 | DOI | MR | Zbl
[5] B. M. Levitan, I. S. Sargsjan, Introduction to spectral theory: selfadjoint ordinary differential operators, Transl. Math. Monogr., 39, Amer. Math. Soc., Providence, RI, 1975, xi+525 pp. | MR | MR | Zbl | Zbl
[6] J.-P. Bourguignon, “Sturm–Liouville equations all of whose solutions are periodic, after F. Neuman”: A. L. Besse, Manifolds all of whose geodesics are closed, Ergeb. Math. Grenzgeb., 93, Springer-Verlag, Berlin–New York, 1978, 225–230 | DOI | MR | MR | Zbl
[7] J. Harris, Algebraic geometry. A first course, Grad. Texts in Math., 133, Springer-Verlag, New York, 1992, xx+328 pp. | DOI | MR | Zbl
[8] Ya. M. Dymarskii, “Manifold method in the eigenvector theory of nonlinear operators”, J. Math. Sci. (N.Y.), 154:5 (2008), 655–815 | DOI | MR | Zbl
[9] L. D. Landau, E. M. Lifshitz, Course of theoretical physics, v. 3, Addison-Wesley Series in Advanced Physics, Quantum mechanics: non-relativistic theory, Pergamon Press Ltd., London–Paris; Addison-Wesley Publishing Co., Inc., Reading, MA, 1958, xii+515 pp. | MR | MR | Zbl | Zbl
[10] V. I. Arnold, Mathematical methods of classical mechanics, Grad. Texts in Math., 60, Springer-Verlag, New York–Heidelberg, 1978, xvi+462 pp. | DOI | MR | MR | Zbl | Zbl
[11] N. I. Akhiezer, “Nekotorye obratnye zadachi spektralnogo analiza, svyazannye s giperellipticheskimi integralami”, Prilozhenie v kn.: N. I. Akhiezer, I. M. Glazman, Teoriya lineinykh operatorov v gilbertovom prostranstve, v. 2, 3-e izd., ispr. i dop., Vischa shkola, Kharkov, 1978, 242–283 | MR